It is often said that inverted yield curves $($with long$-$term yields lower than shortterm yields$)$ forecast upcoming recessions. Let's think through the logic of it$.$

For simplicity, just consider one and two$-$year bonds. Their annual bond yields are given by ${?}_1{R}_1$ and ${?}_1{R}_2,$ respectively. Let $E{(}_2{r}_1)$ denote the current market expectation fo the one$-$year interest rate next year. To avoid confusion, the timing span over which these interest rate variables operate are drawn in the Figure below.

$($a$)(2$ points$)$ Suppose ${?}_1{R}_2=4\%$ and ${?}_1{R}_1=5\%.$ Assume that unbiased expectation hypothesis is true. What is $E{(}_2{r}_1)?($Please show the process of numerically solving for it$.)$

$($b$)(2$ point$)$ Is the current yield curve inverted?

$($c$)(3$ points$)$ Now, let's recall that the Fed sets short$-$term $($i$.$e$.$ one$-$year$)$ interest rates. That is$,$ in one year's time, the Fed will set the one$-$year interest rate at that time based on its understanding of the macroeconomy as of that time. Also recall that one of the Fed's main objective is to sustain high employment through setting interest rates, as well as the fact that periods with good economy $($no recession$)$ tend to have good employment.

Given all these information, please articulate why an inverted yield curve may indicate that market participants foresee a future recession $($which is one$-$yearlater in our specific example$).$ Please make your articulation as clear and as logical as possible.